Usually (or very often), good Protoss players, after building a Robotics bay, build observer and put it to opponent base.

From my perspective if you know Protoss build Robo you should care about that observer.

How do I most effectively deny this observer?

The most often I play Terran and there are few ways for that:

Scan your choke and kill observer with marines. This can fail if observer is not in the scanned screen. That also cost you 50 energy (270 minerals). Observer costs 25/75... if we take gas/mineral exchange rate as 2.5 - it is pretty good price for killing observer...

Build Engineering Bay and build few turrets. that costs 150+x*75... also not too bad. This will take time, but could be also useful in a long run (detect DT or other observers, some defense against phenixes and VoidRays).

Build Raven (if you have StarPort with tech lab). That costs 100/200 - a little bit expensive for observer hunting, but you could later use Raven for PDD, etc...

Some time passed from the question, for now my observations for high level players tell me that if you playing Terran vs Protoss and detected observer - immediately get your 3-5 closest marines, use scanner and kill observer.

Yes, this way is more expensive then building turret (270 minerals vs 100), not a 'long-term' investment, but work right now and provide 100% guarantee on success. In case of turret building opponent can get observer back, etc.
This 'investment' is worth as it force opponent to build another observer (45 seconds, and some money) instead of building Immortal/Colossus.

Due to these reason I would say that is the best method to deal with opponent observers if you don't have turret/Raven right now.

P.S.
Once I figure out answers on other own questions, I will add them here.

Do note that static defense should never be considered where a mobile defense is an option, and in the Terrans case, a Raven may appear costly at first, but it's versatility (and mobility), in terms of a car mileage analogy, goes a loooooong way.

But yeah, having Turrets (for Terrans), Photon Canons (Protoss) or Spore Crawlers (Zergs) around your base should deter any observer from observing at will, and should help you hunt for them sufficiently -- then again, do note that it's okay for your opponent to find out what your tech tree will be, as long as you 'power up' faster and attack swiftly, leaving your opponent with little time to react.

Terran:
If it's in your base, probably just make a turret, it ends up being cheaper than a scan. If you want one in outside your base then maybe consider ravens if it fits with the rest of your strat, otherwise just scan.

With Zerg probably overseer. You mentioned what if you don't have a lair? The question is why don't you have one? There are legitimate reasons, like you're going for a big early-mid game push with low tech, that's fine, but then by the time they get an observer it's usually too late. Otherwise you usually have a lair about the same time or before they get observers. Remember it's Pool -> Lair, whereas it's Gateway -> Core -> Robo so that's higher in the tech tree.

For Toss, having your own observers is generally good anyway, but unless you're going air, you should have a forge at some point to upgrade. (Actually that applies to all races, except maybe Terran if you're going Mech in which case you're upgrading from the armory) If you are going fast air, then that's probably just bad luck that they saw it, but I haven't seen many toss go air since the void ray changes.

Before you do any of that though, you should determine first off, are you actually trying to hide anything? Are you going to be doing anything that would make your opponent change their plan based on seeing it. If not, then maybe you can just let the obs sit there for a while. Don't need to take time to deviate from your normal plan to stop them from seeing something they could've guessed already without seeing.

I like an idea to think "if you really need to hide anything". But, if opponent patrol you base with 2 observers he can know "nothing special" is coming... To handle that we could build some building structure in other locations... but wouldn't be better to hide everything from opponent and let him think "if everything is still ok"? Probably this way I will force him to build 2 more observers instead of 1 immortal...
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BuddaFeb 28 '11 at 18:22

if you do your trick and build 'surprise-giving' buildings not on base and ALSO kill observers scouting your base - you will force opponent to send new observers to YOUR base. Otherwise he could try to find surprises in other places... It is always good to hide information... but also much better to provide wrong information ;) I like StarCraft!!! It is a really craft!
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BuddaFeb 28 '11 at 18:26

I think that question is how to find observer w/o scan.
If you suspect that you have a observer staying still in your base then try to find it by rotating camera (mouse wheel or Ins / Del) in 2-3 "popular" places - you'll notice texture distortion caused by cloak effect. Then scan & kill.
Ravens are great support against protoss army (deny obs and disable stalkers) so consider to build one

I know how to find observer w/o scan... the question is how to detect him to be killable. Using Zerg if you don't have lair? You can also build spore colony (don't remember building name) and with Protoss - cannon... but my question - if you don't have neither Robo no Forge - what would you build to get detector? Should Protoss build forge/Robo always (just for case), etc. That is an answer I would expect.
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BuddaFeb 28 '11 at 14:10

@budda: If you're playing solo, with the protoss, you should always make sure you have a detector. You can throw down cannons, or build observers, but you could be in serious trouble without some method of detection. Banshees, Roaches, and DT's oh my!
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SatanicpuppyFeb 28 '11 at 15:32

@budda: as Gweebz said mobile detection is better that static. You cannot cover all your base with turrets / cannons / spore crawlers. May be your question was: "how to hide my tech" but not "countering observers"?
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MetaMar 1 '11 at 6:10

No, for this particular question I would like to analyze ways to kill observers (not hide something, not provide wrong information to the opponent). Just kill them in the most easy, chip, and effective way.
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BuddaMar 3 '11 at 15:13